The "moment of truth" in Brexit negotiations is approaching and the European Union hopes for agreement on so-called withdrawal issues "in the next few days", Brussels' chief negotiator has said.

Michel Barnier called for "real, sufficient progress" on the Brexit "divorce bill", citizens' rights and the Irish border, so that EU leaders can green-light talks on trade and a transition period before Christmas.

He spoke as Ireland's foreign minister Simon Coveney stressed that all EU27 leaders agree that trade talks cannot start unless Britain offers further assurances there will be no hard border with Northern Ireland.

Prime Minister Theresa May has been given until December 4 to come up with further proposals on the withdrawal issues so Mr Barnier can recommend to leaders at the December 14-15 European Council summit that enough progress has been made for trade talks to begin.

At an EU summit in Tallinn, Estonia, Mr Barnier said: "I do hope in the next few days we will come up with an agreement on principles, and a real agreement.

"We need to have real, sufficient progress in the three key areas where the UK's decision has created a lot of uncertainty and fear even."

He added: "The moment of truth is approaching, we have a council under the Estonian presidency on December 14 and 15, and I really hope that will be the point where we will see real, sufficient progress on the conditions of our separation.

"And that will allow me to recommend the opening up of the next two phases of negotiations, first of all on the transition period and then on the future relationship."

Amid fears there could be a return to a hard border in Ireland given the UK Government's commitment to leaving the European single market and customs union, which allow for frictionless trade, the Frenchman said: "We don't want to be putting up barriers again and we need furthermore to maintain the integrity of the single market."

On the divorce bill, he said Britain must honour its commitments for the EU budget between 2014 and 2020, which Mrs May has already signalled she will do.

"We have a programme from 2014 to 2020 and I have said we are not willing to pay, the 27 are not willing to pay what has been decided by the 28 and so we are asking for the UK to play its part, to honour its commitments for that period," Mr Barnier said.

And on the rights of EU nationals in the UK and British expats in Europe, he said: "We have done a lot, but we need to ensure that we clearly secure their rights reciprocally and that's why we need a role for the European Court of Justice."

Mr Coveney said Ireland will not need to use its veto to prevent progress in talks because EU negotiators will block it themselves if the UK does not offer a workable solution on the Irish border.

He said he had received personal assurances from senior EU figures Mr Barnier, Donald Tusk and Jean-Claude Juncker on Friday that Brussels would hold firm on this demand.

"They have repeated the message that Ireland's problems are the EU's problem, so Ireland is not going to be isolated and forced to use a veto," said Mr Coveney.

EU leaders insist a hardening of the border is inevitable if the UK leaves the single market and customs union, as checks will be required to monitor movement between jurisdictions operating under two different regulatory systems.

One solution offered by Europe is the suggestion Northern Ireland would continue to comply with EU regulations post-Brexit but this has been rejected by the UK Government.

Any arrangement which appeared to give Northern Ireland a separate status would also be strongly resisted by the Democratic Unionists (DUP), whose 10 MPs are effectively keeping Mrs May in Downing Street after she lost her majority in the general election.

Asked about the prospect of movement on the border issue, the PM's official spokesman said Britain is "firmly committed" to avoiding a physical frontier.

He added: "In order to be able to see what the solution is going to finally look like, we need to understand what the future trading relationship is going to be, because the two things are obviously related. We want to get on to talking about trade as soon as possible."

The PM's spokesman gave short shrift to suggestions that the problem could be resolved by allowing Northern Ireland to continue to observe the rules of the customs union, saying: "This has been raised numerous times and we've been clear that the United Kingdom as a whole is leaving the single market and is leaving the customs union."

He added: "We have reached agreement on continuing free movement of people over the border and we are focusing on finding a solution in relation to goods."

Former taoiseach Bertie Ahern has suggested the only solution is to introduce technology to manage multinational trade while turning a blind eye to lower-level cross-frontier movement in areas such as agriculture.